Becoming a U.S. citizen demands allegiance to the U.S. over any other country (such as during a war) and the U.S. does not recognize dual citizenship. A naturalized U.S. citizen is, in the eyes of the federal government, a U.S. citizen only. However, there are many countries in the world that recognize dual citizenship. If France recognizes dual citizenship, then your husband will not "lose" his French citizenship. France will always recognize his status as a citizen of her country. The U.S. doesn't have the power to "take away" your citizenship to another country, but does have the power to demand your allegiance to itself and will expect affirmative answers to the questions in the last section of the N-400 regarding attachment to the U.S. Constitution and government and such in order to approve a naturalization applicant. Your husband can inquire with his embassy or consulate regarding dual citizenship recognition. If he has further questions, have him consult with an experienced naturalization attorney. Bonne chance!